Answer:
Step-by-step explanation:
To graph the functions y = sin^(-1) x and y = π - sin^(-1) x on the same coordinate-axis system, we can use the properties of the inverse sine function and the unit circle.
The inverse sine function, denoted as sin^(-1) x or arcsin x, is the inverse of the sine function. This means that if we input a value x into the inverse sine function, it will output the angle θ in radians that satisfies the equation sin θ = x.
The unit circle is a circle with radius 1 centered at the origin of a coordinate plane. The angles in the unit circle are measured in radians. On the unit circle, the x-coordinate of a point is equal to the cosine of the angle formed by the point and the positive x-axis, and the y-coordinate is equal to the sine of the angle.
Given this information, we can graph the functions y = sin^(-1) x and y = π - sin^(-1) x as follows:
For y = sin^(-1) x, we can input values of x into the inverse sine function and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, -π/2), (1, π/2), and (0, 0).
For y = π - sin^(-1) x, we can input values of x into the inverse sine function, subtract the resulting values from π, and plot the resulting values of y on the coordinate plane. Since the range of the inverse sine function is -π/2 ≤ y ≤ π/2, we can start by plotting the points (-1, π/2), (1, -π/2), and (0, π).
On the same coordinate-axis system, the graph of y = sin^(-1) x will be a curve that starts at (-1, -π/2), goes through (0, 0), and ends at (1, π/2). The graph of y = π - sin^(-1) x will be a curve that starts at (-1, π/2), goes through (0, π), and ends at (1, -π/2).
If we connect the points on the two curves, we will see that they intersect at (0, π/2) and (0, -π/2). This means that the two functions are reflections of each other about the x-axis.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75.
The sales tax rate in her county is 7%. How much will Cassie pay in all for
the pair of binoculars after sales tax is included? Round to the nearest cent
if necessary.
$10.12 will Cassie pay in all for the pair of binoculars after sales tax is included.
What is sales tax?
A sales tax is a fee that is paid to the government when specified products and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are often used to describe taxes on goods and services that consumers pay directly to a governing authority.
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
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Consider the sample space given below. A die is a cube with six sides and each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray.S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66)a) Let E be the event that the sum of the numbers showing face up is equal to 6. Write E as a set. (Write your answer in set-roster notation.) b) What is the probability of e? c) Let F be the event that the sum of the numbers showing face up is at most 4. Write Fas a set. (Write your answer in set-roster notation. ) d) What is the probability of F? Show all work in either the answer box shown or upload your answer with a file - can be PDF or jpeg only.
a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:
E = {11, 15, 24, 33, 42, 51}
b) The probability of E is 6/36 = 1/6.
c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:
F = {11, 15, 22, 31, 33, 42, 44, 51}
d) The probability of F is 2/9.
Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.
The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.
So, the probability of E is 6/36 = 1/6.
The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.
So, the probability of F is 8/36 = 2/9.
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an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
sketch the region enclosed by the given curves (within the given bounds, if provided) and find its area.
The area enclosed by the curves f(x) and g(x) is 1/12
Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.
When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.
Let our given curves be :
f(x) = x² and g(x) = x³ within the interval [0,1]
Formula to calculate area under these curves is
=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]
Interval is given from 0 to 1
Therefore ,
=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]
Integrating,
=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]
=> 1/3 - 1/4
=> 1/12 is required area
The given question is incomplete So, I've answered the question in general
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Solve for S
3/ -s + 1 = 6/ s + 4
Answers fast please I need them fast
The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
What are similar triangles?When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.
Given are the similar triangles,
1) Δ HJG ~ Δ CAB
Scale factor = 3:1
2) Δ NPM ~ Δ ABC
Scale factor = 1:2
3) KJML ~ CDAB
Scale factor = 1:2
4) 40/x = 20/5
x = 10
5) 18/x = 21/7
x = 6
6) 6/3 = x/15
x = 30
Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
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if you were to add 25 to y what would you get in all?
Answer:
25 + y
Step-by-step explanation:
It looks like you might be missing some information.
David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Answer: Susie is correct.
Step-by-step explanation:
Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.
a²+b² = c²
a = 9
b = 12
c = 17
9² + 12² = 17²
==> 81 + 144 = 289
==> 225 = 289, This is not true
Therefore this triangle is not a right triangle.
1. Which property justifies the second line in the following solution?
(1) Multiplicative Property of Equality
(3) Distributive
(2) Associative
(4) Additive Property of Equality
3x+2=8
3x+2-2=8-2
Additive Property of Equality justifies the second line in the 3x + 2 = 8
3x+ 2 - 2 = 8 - 2 solution.
What is Multiplicative Property of Equality?
When we multiply on both sides of an equation then the equation is remain same.
Distributive property: a(b + c) = ab + ac in other words the product of a number with sum of two numbers is equal to the sum of product first two numbers and "first and third" numbers.
Associative property: (a + b) + c = a + (b + c): If we shift the parenthesis then the result will remain the same.
Given equation is
3x+2=8
The second step is 3x + 2 - 2 = 8 - 2.
The additive inverse of 2 is -2.
-2 is added in second step. Thus Additive Property of Equality is used.
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How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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Problems 14 and 15 pertain to the following situation: a woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%.
14. The probability that in any one month at least three of the tickets that the woman buys are winning tickets is about?
15. The average number of winning tickets that the woman buys each month is about?
The required probability is P(X≥3) =0.3234
The average number of winning tickets that the woman buys each month is 2.
The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.
The probability mass function of the binomial distribution is defined as:
[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]
Given that,
n = 20
p = 0.10
The required probability is P(X≥3)
P(X≥3) = 1-P(X<3)
P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)
P(X≥3)= 1- 0.1216- 0.270- 0.285
P(X≥3) = 0.3234
The mean of the distribution is defined as μ=n*p= 20*0.10= 2
The average number of winning tickets that the woman buys each month is 2.
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Work out the bearing of C from A
The bearing of C from A is 60° South.
How does one calculate bearing from A to B?
The bearing from A to B can be determined using interior angle if the bearing from B to A is known. Use the fact that angles in a full turn add up to 360° to determine the bearing of A to B, then subtract the bearing of B to A from 180° to determine the missing interior angle. For instance, B is 050° from A in terms of bearing.When AN elongates the angle will be 180°
Then the angle between A and C:
35° + 85° + x = 180°
120° + x = 180°
x = 180° - 120°
x = 60°
Hence, The bearing of C from A is 60° South.
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Screen time Administrators ata small school with 200 students want to estimate the average amount of time students spend looking ata screen (phone, computer; television, and s0 on) per day: The adminis- trators select a random sample of 50 students from the school to ask: (a) Show that the 10% condition is not met in this case_ (b) What effect does violating the 10% condition have on the standard deviation of the sampling distribution ofx?
10% condition is not met in this case because here sample size if 10% of the population is taken = 20.
Standard deviation decreases if 10% condition is violated.
What is 10% condition?10% condition states that the sample size we are working with must not exceed the population size. It is mostly useful when we are working with samples which are not independent.
If we use the 10% condition even with samples which are not actually independent, this condition will make it seem independent.
(a) Here population size = 200
Sample size = 50
If the 10% condition is met, sample size = 10% of population size
= 0.10 × 200
= 20
Sample size has exceeded the 10% condition.
(b) Standard deviation measures how much the set of values differ from it's mean value.
Violating 10% condition increases the sample size which in turn decreases the standard deviation.
Hence the 10% condition has not met in this case as the sample size is larger. Standard deviation decreases if 10% condition is violated.
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Wei Jing has between 70 and 150 baseball
cards in his collection. When he arranges them
in groups of 10, he has 3 left over. When he
arranges them in groups of 9, he has 5 left
over. If he arranges them in groups of 8, how
many will he have left over?
Answer:
117$.
Step-by-step explanation:
Let $x$ represent the number of cards in Wei Jing's collection. We are given that $70 \leq x \leq 150$. We are also given that $x \equiv 3 \pmod{10}$ and $x \equiv 5 \pmod{9}$. Since $x \equiv 3 \pmod{10}$, $x - 3$ is divisible by 10. Since $x \equiv 5 \pmod{9}$, $x - 5$ is divisible by 9. The least common multiple of 10 and 9 is $90$, so $(x - 3) - 90$ is divisible by 90 and $(x - 5) - 90$ is divisible by 90. Adding these equations gives us $2x - 98$ is divisible by 90. Dividing both sides by 2 gives us $x - 49$ is divisible by 45. Since $70 \leq x \leq 150$, the only solution for $x$ is $x = 117$.
A survey shows that the probability that an employee gets placed in a suitable job is 0.65. A psychometric test consultant claims that he could help place any employee in a suitable job based on the result of a psychometric test. The test has an accuracy rate of 70%. An employee working in a particular company takes the test. The probability that the employee is in the right job and the test predicts that he is in the wrong job is . The probability that the employee is in the wrong job and the test predicts that he is in the right job is
The probability that someone is in the right job and the test is then wrong is 0.195.
The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In
The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3. Thus, the probability that someone is in the right job and the test is then wrong is:
= 0.65*0.3
= 0.195
The probability that someone is in the wrong job and the test is right is:
= 0.35 × 0.3
= 0.105.
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A recent study Indicated that 27% of the 142 women over age 55 in the study were widows
A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.
What is standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows
Margin of error = 0.05 = E
z-score = z/2 = 1.645
n = 0.27 x 0.73 (1.645/ 0.05)²
n = 213.343
n=214
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find xand y if x(1,1)+y(2,-1)=(1,4)
The value of the variables x and y according to the given representation as required are; 3 and -1 respectively.
What are the values of variables x and y according to the given information?It follows from the task content that the values of the variables x and y are to be determined according to the given representation.
Since the given representation is;
x( 1, 1 ) + y( 2, -1 ) = ( 1, 4 )
The system of equations which correctly represents the situation is;
x + 2y = 1..........(i)
x - y = 4............(ii)
By subtracting equation (ii) from equation (i); we have;
2y - (-y) = 1 - 4
3y = -3
y = -3 / 3
y = -1.
On this note, by substitution into the equation (ii);
x - (-1) = 4
x + 1 = 4
x = 4 - 1
x = 3.
On this note, the values of x and y as required in the task content are; 3 and -1 respectively.
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The mass of a cube,
M
(kg), is proportional to the cube of the length of its edge,
L
(m).
The mass of the cube is 90 kg when the length of its edge is 20 cm.
Work out
L
(to 2 DP) when
M
=
1700
kg
Answer:
Below
Step-by-step explanation:
m = k l^3 <=======given
when m = 90 kg and l = 20 cm
90 = k (20^3) shows k = .01125 kg/cm^3
sooooo : m = .01125 l^3
when m = 1700:
1700 = .01125 l^3
l = cubrt ( 1700/.01125) = 53.26 cm
Suppose that the relation G is defined as follows G={(-6, -4), (5, -4), (1, 5) give the domain and range of G Write your answers using set notation
Suppose that the relation G is defined as follows G={(-6, -4), (5, -4), (1, 5) give the domain and range of G in set notation
domain {-6, 5, 1}
range {-4, -4, 1}
What is set notation?In mathematics, set notation is essentially a list of numbers, things, or results. Curly brackets, often known as braces, are used for set notation.
The items included between brackets are referred to as elements of a set and are not required to be in any particular order.
How to find the domain and the rangeAll of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
in the given relation, G={(-6, -4), (5, -4), (1, 5)}
the first figure in the parenthesis is the domai whilel the next is the range
hence domain = -6, 5, and 1 while range is -4, -4, and 5
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NO LINKS!! Please help me with this problem. Part 2gg
Answer:
Answer please see analysis
(I am not sure)Answer:
See attachment.
Step-by-step explanation:
The double brackets [[x]] denote the function is a floor function.
It also (more commonly) written as ⌊x⌋.
The definition of a floor function is "the greatest integer that is less than or equal to x".
Parent floor function
f(x) = ⌊x⌋
The graph of the parent floor function has closed dots at (x, x) and open dots at (x, x-1). Each segment is joined with a horizontal line (step).
The closed dot means the value is included, whereas the open dot means the value is not included.
Given floor function:
g(x) = -[[x]] = -⌊x⌋
As the given floor function is negative, it is a reflection of the parent floor function in the x-axis.
Therefore, the graph of the given function has closed dots at (x, -x) and open dots at (x, -(x-1)). Each segment is joined with a horizontal line (step).
To draw the graph with the restricted domain [0, 5):
Place closed dots at (0, 0), (1, -1), (2, -2), (3, -3) and (4, -4).Place open dots at (1, 0), (2, -1), (3, -2), (4, -3) and (5, -4).Join each pair of closed and open dots (with the same y-value) with a horizontal line (step).Note
The first attachment (green graph) is the graph of the given function g(x).
The second attachment (black graph) is the graph of the parent floor function for information purposes only.
Your class council determined that its profit from the upcoming homecoming dance is directly
related to the ticket price for the dance. Looking at past dances, the council determined that the
profit p can be modeled by the function p(t) = -1212 + 480t + 30, where t represents the price of
each ticket. What should be the price of a ticket to the homecoming dance to maximize the
council's profit?
The price of a ticket to the homecoming dance to maximize the council's profit is 4830.
Define vertex?A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.The vertex of an angle is the point around which it is measured, and the vertex angle is the angle that corresponds to a particular vertex.A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the shape.Given: a= -12, b = 480Vertex t= -b/2at= -480/2(-12) = 20Therefore, $20 per ticket.p(20) = -12(20) pow 2 + 480(20) + 30= 4830To learn more about vertex refer to:
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Answer:
$2 each ticket
Step-by-step explanation:
I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.
Jocelyn estimate that a piece of wood measure 5.5 cm . If it actually measure 5.62 cm, what is the percent error of Jocelyn's estimate
The Jocelyn estimate's percent error is 2.181 centimeters..
What is percent error ?
Percent error calculates the difference between an estimate and a right number and expresses it as a percentage. Analysts can use this statistic to determine how big the mistake is in relation to the actual number. It is also referred to as % error and percentage error.
There are three steps to determining the % error:
1. Determine the error, which is the estimated value minus the actual value.
2. Multiply by the accurate value.
3. In order to create a percentage, multiply by 100.
Given information:
The size of a piece of wood (Exact value)= 5.5 cm
if it really does measure(Approximate value)=5.62 cm
percentage error={(approximate value-exact value)/exact value}×100
percentage error = ((5.62-5.5)/5.5)×100
percentage error = 2.181cm
Consequently, 2.181cm is the Jocelyn estimate's percent error.
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What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inwhich properties of equality do you use to solve the
equation 15 =x/3 + 18?
The adding property of equality should be used to satisfy the given equation.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-15 + x/3 = 18
Add 15 on both sides of the equation
So, we have
45 + x = 18 × 3
x = 54 + 45
x = 99
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If 1+3+5+7+…+49 =625, what is 2+4+6+8+…+50?
If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.
What is arithmetic series?
A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Here, we have
Given: 1+3+5+7+…+49 =625
We have to find the value of 2+4+6+8+…+50.
Here, we calculate the sum of all even numbers and we get
2+4+6+8+…+50 = 650
Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.
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solve for the missing angle, must show all your work
help pleasee
Answer:
Step-by-step explanation:
cos x = 7/10
x= cos^-1 7/10
x=45.57
Which equation represents the line that passes through the point (5,7) and is parallel to the graph of y=2/3x-7?
The equation of a line that passes through point (5,7) and parallel to the graph of y = 2/3x - 7 is y = (2/3)x + 11/3
What is the equation of line that passes through the point (5,7) and is parallel to the line y = 2/3x - 7?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Where m is slope.
Given the equation of the graph y = (2/3)x - 7
Using the slope intercept form where m is slope.
y = mx + b
y = (2/3)x - 7
Slope of the graph will be;
Slope m = 2/3
Next, find the line parallel to the graph and which passes through the point (5,7).
Using the point slope formula
y - y₁ = m( x - x₁ )
Plug in the slope and point.
y - 7 = (2/3)( x - 5 )
Solve for y
y - 7 = (2/3)x - 10/3
y = (2/3)x - 10/3 + 7
y = (2/3)x + 11/3
Therefore, the equation of line parallel to the graph is y = (2/3)x + 11/3.
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Find the measure of the exterior angle:_______
The measure of the exterior angle is 60°.
What is the Exterior Angle Theorem?
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
We have,
interior angles:
∠ABC = z + 10
∠BAC = 4z
Exterior angle:
∠ACB = z + 50
Exterior Angle Theorem:
The measure of exterior angle = Sum of two opposite interior angles’ measure.
According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠BAC would be equal to the exterior angle ∠ACB.
∴ ∠ABC + ∠BAC = ∠ACB
z + 10 + 4z = z + 50
5z = z + 40
z = 40/4
∴ z = 10
so, the value of the z is 10.
exterior angle:
∠ACB = 10 + 50 =60
Hence, the measure of the exterior angle is 60°.
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
The given triangles are congruent to each other by the rule of (AAS) Angle Angle side.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given figure in the question,
There are two given triangles in the question,
Δ ABC and Δ MNO
As we can see that,
∠ C = ∠ M
∠ B = ∠ N and,
The side, AC = OM
So, Δ ABC ≅ Δ MNO
So, by using AAS (Angle Angle Side) rule, triangle ABC and triangle MNO are congruent to each other.
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